Which of the following is a binomial ?

Options

A. `7 xx a+ a`
B. `6a ^(2) + 7b + 2c`
C. `4a xx 3b xx 2c`
D. `6 (a ^(2) + b) `

Answer

To determine which of the given options is a binomial, we need to understand what a binomial is. A binomial is an algebraic expression that contains exactly two terms. Let's analyze each option step by step.

### Step-by-Step Solution:

1. **Option 1: \( 7a + a \)**
- Combine the terms: \( 7a + a = 8a \).
- This results in a single term (8a).
- **Conclusion**: This is not a binomial (it is a monomial).

2. **Option 2: \( 6a^2 + 7b + 2c \)**
- Count the terms: \( 6a^2 \), \( 7b \), and \( 2c \).
- There are three distinct terms.
- **Conclusion**: This is not a binomial (it is a trinomial).

3. **Option 3: \( 4A \times 3B \times 2C \)**
- Multiply the coefficients: \( 4 \times 3 \times 2 = 24 \).
- Combine the variables: \( A \times B \times C = ABC \).
- This results in \( 24ABC \), which is a single term.
- **Conclusion**: This is not a binomial (it is a monomial).

4. **Option 4: \( 6a^2 + 6b \)**
- Identify the terms: \( 6a^2 \) and \( 6b \).
- There are two distinct terms.
- **Conclusion**: This is a binomial.

### Final Answer:
The correct option that is a binomial is **Option 4: \( 6a^2 + 6b \)**.

---